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Originally Posted by harmonygirl Michelle,
I don't think that seeds contain themselves, they contain information that lead to their formation. I think Dustin's example was a sound one: a cookie contains ingredients (flour, sugar, eggs and butter-and hopefully chocolate!) but the ingredients of a cookie do not contain a cookie. A set of things (whatever those things are) may or may not contain itself (a bag of bags, etc) but does the set of all sets contain itself? |
None of these four forms are russell's paradox:
'a cookie contains ingredients' is a set that contains it's members. Well then yes, because all sets contain the members that contain themselves.
'but the ingredietns of a cookie do not contain a cookie' this is a deep metaphysical discussion. Many philosophers believe that they do, that everything contains it's own cause, or, in this case, it's container. And anyway, weren't those ingredients determined to end up forming part of the cookie? If I had seen them, they woul dbe determined, I couldn't have stopped it.
'a set of things may or may not contain itself ' well this is harder to tell. The thing is that int he example of the cookie it actually doesn't contain itself, it contains it's members. There is a wrong interpretation by you all: all sets contain themslves in that they contain all their members and these are the set, but this is not containing itself, it's just being itself. And every set is itself, it's members. The containing about which russell' paradox is about is that a set's cnditions for members includes the set itself. A cookie doesn't contain itself in here, for a cookie doesn't condition a cookie, but the ingredients. You may set 'well yes, but it could be simply conditioning the cookie' well this is true, but irrelevant. The problem in the whole of this discussison is what we consider member and what we consider set. Because normally I look at cookies more like entities, like members of a set of cookies, than sets of ingredients. And here is the main problem of set-ting.
'but does the set of all sets contain itself?' This again isn't russell. Russell's paradox is:
The set of all sets that do not contain themselves contains itself if it does not contain itself, and does not contain itself if it contains itself. The set of all sets contains itself obviouslyl as it is a set. of all sets means all, including the empty sets, and the set of sets and even russell's set.